When it starts acting up like that, spray some ether, or carburetor cleaner around the adapters and mounting flange for the carburetor, and report back as to what happens.
I am betting that you have a vacuum leak, that when the engine is cold it is more pronounced and when the engine is warmed up, the leak is not as severe due to things expanding as they get heat into them.
The bolts shipped with the adapter, that attach the top adapter plate to the lower plate are too long, and if not shortened up before installing, will pass through the lower adapter that they thread into, and cause the lower adapter to be pried up off the intake, creating at the very least a vacuum leak, and more likely than not, fracturing the lower adapter plate. This has been the case since the very first Weber I installed on my junk back in 1992, and is something that I have addressed with every Weber I have installed since. (At least 25, the most recent being last spring, and the bolts are still too long)
Post up what you find out...